Tuesday could be the day that senators find out how much different the chamber may operate in the 113th Congress than it did in the 112th when it comes to filibusters.

A delay in resolving changes in filibuster rules could throw a monkey wrench into any other business, including aid to victims of Superstorm Sandy.

Senate Majority Leader Harry Reid, D-Nev., is likely to discuss the possibilities for changing the chamber’s rules regarding limitations on debate at a Democratic caucus lunch Tuesday, which could set the stage for a consensus agreement or a procedural stalemate.

Sen. Dianne Feinstein, D-Calif., said she understands that a proposal will be made Tuesday and she hopes the two parties can reach a compromise without Democrats needing to resort to the “nuclear” option. “I’m looking forward to the meeting on Tuesday,” she said.

During the chamber’s break between the swearing-in of new senators on Jan. 3 and Monday’s inaugural ceremonies, Reid spoke about his thinking on ways to change Senate rules to increase the chamber’s efficiency, suggesting he wants to enact a more narrow package of filibuster modifications than some of the more liberal members of his caucus favor.

In interviews with Nevada-based media, Reid has signaled that he wants to make three significant changes. One would cut down on the number of potential filibusters for sending bills into House-Senate conference committees, another could curb or eliminate 60-vote requirements on motions to proceed to Senate business and the third could force senators to personally hold the floor to delay action when Reid has already proved he has the 60 votes needed to limit debate.

The rules situation needs to be decided before the chamber can move forward on legislative business, Democratic leadership aides have said. Reid has kept the Senate in its first legislative day and not explicitly acquiesced to the rules in place during the 112th Congress to preserve his ability to change the rules with only a simple majority vote if he cannot reach agreement with Minority Leader Mitch McConnell, R-Ky.

New York Sen. Charles E. Schumer, the no. 3 Democratic leader, has acknowledged that the rules issue could mettle with the timing for Senate consideration of the package to aid victims of the storm, which ravaged Schumer’s home state and its neighbors along the East Coast last year.

“Hopefully we will have a good rules package,” Schumer said during the week the Senate first convened. “You can delay that several more days, I guess.”

The Senate could further extend the first legislative day and continue the procedural limbo until a deal is reached. By some measures, the Senate appears to already be operating under the existing rules as though they were continued.

The House passed a broad $50.5 billion package for disaster relief on Jan. 15, with only 49 members of the House’s Republican majority supporting the measure (HR 152). The package was allowed a vote on the floor after a dispute over scheduling in the final hours of the 112th Congress doomed an earlier Sandy aid bill already passed by the Senate.